Lagrangian method for nonlinear ODE, 2nd order ?

I have to solve non-linear ODE of 2nd order. The Maple routines can't find integrating factor. I think that's connected to Lie symmetries that can't be found.

I'm thinking of getting a Lagrangian for which that equation is the Euler-Lagrange equation and somehow guess a symmetry of the Lagrangian or perhaps choose more appropriate variables in the equation to obtain partial if not general solutions. Essentially that is looking for a Noether symmetry (Lagrangian method) vs Lie symmetry (integrating factor method).